Inversion of electromagnetic induction data using a novel wavelet-based and scale-dependent regularization term. Issue 3 (6th May 2021)

• Record Type: Journal Article
• Authors: Deleersnyder, Wouter; Maveau, Benjamin; Hermans, Thomas; Dudal, David
• Is Part Of: Geophysical journal international. Volume 226:Issue 3(2021)
• Page Start: 1715
• Page End: 1729
• Publication Date: 2021-05-06
• Subjects: Controlled source electromagnetics (CSEM) -- Electromagnetic theory -- Inverse theory -- Wavelet transform; Geophysics -- Periodicals; 550
• DOI: 10.1093/gji/ggab182
• Languages: English
• ISSNs: 0956-540X

Abstract

SUMMARY: The inversion of electromagnetic induction data to a conductivity profile is an ill-posed problem. Regularization improves the stability of the inversion and a smoothing constraint is typically used. However, the conductivity profiles are not always expected to be smooth. Here, we develop a new inversion scheme in which we transform the model to the wavelet space and impose a sparsity constraint. This sparsity constrained inversion scheme will minimize an objective function with a least-squares data misfit and a sparsity measure of the model in the wavelet domain. A model transform to the wavelet domain allows to investigate the temporal resolution (periodicities at different frequencies) and spatial resolution (location of the peaks) characteristics of the model, and penalizing small-scale coefficients effectively reduces the complexity of the model. The novel scale-dependent regularization term can be used to favour either blocky or smooth structures, as well as high-amplitude models in globally smooth structures in the inversion. Depending on the expected conductivity profile, a suitable wavelet basis function can be chosen. The scheme supports multiple types of regularization with the same algorithm and is thus flexible. Finally, we apply this new scheme on a frequency domain electromagnetic sounding data set, but the scheme could equally apply to any other 1-D geophysical method.